Constrained Nonlinear Regression

Notes

 | -------------------------------------------- | ------------------------------------------------------ | 
 | Output Created                               | 22-APR-2002 18:03:45                                   | 
 | -------------------------------------------- | ------------------------------------------------------ | 
 | Comments                                     |                                                        | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 
 | Input       | Data                           | N:\YTO\TCDD\ABC kannat\SPSS\s242_abc_spss.sav          | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | Filter                         | WLA                                                    | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | Weight                         | <none>                                                 | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | Split File                     | <none>                                                 | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | N of Rows in Working Data File | 70                                                     | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 
 | Syntax                                       | MODEL PROGRAM ED=1 GSD=.5 EMIN=0 EMAX=3 .              | 
 |                                              | COMPUTE PRED_ =                                        | 
 |                                              | emin+(emax-emin)*(CDF.NORMAL(lg10(dose),ed,gsd)).      | 
 |                                              | CNLR toothdef                                          | 
 |                                              | /OUTFILE='C:\TEMP\spss158\SPSSFNLR.TMP'                | 
 |                                              | /PRED PRED_                                            | 
 |                                              | /BOUNDS ED <= 4; ED >= -2; GSD <= 50; GSD >= .01; EMIN | 
 |                                              | >= 0                                                   | 
 |                                              | /CRITERIA STEPLIMIT 2 ISTEP 1E+20 .                    | 
 |                                              |                                                        | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 
 | Resources   | Elapsed Time                   | 0:00:00.16                                             | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 


All the derivatives will be calculated numerically.




  Iteration Residual SS          ED         GSD        EMIN        EMAX

     0.3    64.16280078  1.00000000  .500000000  .000000000  3.00000000
     1.2    62.40077082  1.09565247  1.52099450  .907712415  1.79933045
     2.1    53.99843848  2.09901240  2.94503312  .594126575  3.38501252
     3.4    47.10456867  2.52597648  2.56377237  .460685038  3.42001700
     4.1    46.41643255  2.54772051  2.22476225  .549428590  3.36338162
     5.1    42.83077132  2.31153470  1.32371834  .594000404  3.22432765
     6.1    42.09374745  2.21512811  1.21657946  .568865166  3.19535209
     7.1    40.47879127  1.95138579  .891066369  .567967267  3.03139573
     8.1    39.46501300  1.70194971  .780020744  .508254804  2.88905064
     9.2    38.96979859  1.60142908  .621291709  .529596938  2.80058855
    10.1    38.72872696  1.43427000  .365332973  .624965580  2.57466424
    11.1    38.41606066  1.55140750  .403033528  .621821375  2.64880444
    12.1    38.31680907  1.56894333  .493942185  .604281970  2.65584837
    13.1    38.17773418  1.55301624  .455591738  .587505564  2.60179035
    14.1    38.13934255  1.54527961  .416980030  .596861943  2.54354024
    15.1    38.13771592  1.54771331  .423827093  .591490720  2.55231840
    16.1    38.13770162  1.54780918  .423585532  .592131921  2.55213976
    17.1    38.13770157  1.54781460  .423545406  .592119777  2.55210939

Run stopped after 17 major iterations.
Optimal solution found.


Nonlinear Regression Summary Statistics     Dependent Variable TOOTHDEF

  Source                 DF  Sum of Squares  Mean Square

  Regression              4      169.36230       42.34057
  Residual               66       38.13770         .57784
  Uncorrected Total      70      207.50000

  (Corrected Total)      69       89.20000

  R squared = 1 - Residual SS / Corrected SS =     .57245

                                           Asymptotic 95 %
                          Asymptotic     Confidence Interval
  Parameter   Estimate    Std. Error     Lower         Upper

  ED         1.547814603   .164553207  1.219273524  1.876355682
  GSD         .423545406   .221247520  -.018189520   .865280333
  EMIN        .592119777   .129555383   .333454109   .850785445
  EMAX       2.552109392   .197581684  2.157624832  2.946593952




  Asymptotic Correlation Matrix of the Parameter Estimates

                  ED       GSD      EMIN      EMAX

  ED          1.0000     .1541     .2700     .4589
  GSD          .1541    1.0000    -.2668     .4180
  EMIN         .2700    -.2668    1.0000    -.0552
  EMAX         .4589     .4180    -.0552    1.0000

Constrained Nonlinear Regression

Notes

 | -------------------------------------------- | ------------------------------------------------------ | 
 | Output Created                               | 22-APR-2002 18:03:45                                   | 
 | -------------------------------------------- | ------------------------------------------------------ | 
 | Comments                                     |                                                        | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 
 | Input       | Data                           | N:\YTO\TCDD\ABC kannat\SPSS\s242_abc_spss.sav          | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | Filter                         | WLB                                                    | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | Weight                         | <none>                                                 | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | Split File                     | <none>                                                 | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | N of Rows in Working Data File | 63                                                     | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 
 | Syntax                                       | MODEL PROGRAM ED=1 GSD=.5 EMIN=0 EMAX=3 .              | 
 |                                              | COMPUTE PRED_ =                                        | 
 |                                              | emin+(emax-emin)*(CDF.NORMAL(lg10(dose),ed,gsd)).      | 
 |                                              | CNLR toothdef                                          | 
 |                                              | /OUTFILE='C:\TEMP\spss158\SPSSFNLR.TMP'                | 
 |                                              | /PRED PRED_                                            | 
 |                                              | /BOUNDS ED <= 4; ED >= -2; GSD <= 50; GSD >= .01; EMIN | 
 |                                              | >= 0                                                   | 
 |                                              | /CRITERIA STEPLIMIT 2 ISTEP 1E+20 .                    | 
 |                                              |                                                        | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 
 | Resources   | Elapsed Time                   | 0:00:00.06                                             | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 


All the derivatives will be calculated numerically.




  Iteration Residual SS          ED         GSD        EMIN        EMAX

     0.2    67.09468678  1.00000000  .500000000  .000000000  3.00000000
     1.2    54.98344005  1.08932351  1.35264905  .000000000  1.70300430
     2.4    48.82764471  2.03134362  1.47957630  .275241295  2.97916975
     3.4    48.47515350  2.06185191  1.43918126  .267675588  2.99210312
     4.3    46.29978971  1.90263119  1.39692668  .000000000  3.09893737
     5.1    42.88467955  1.59766772  .010000000  .263691944  2.51547170
     6.3    42.69488328  1.51674450  .010000000  .257011074  2.47634812
     7.5    37.67701694  1.47977539  .012138440  .261161271  2.46144676
     8.1    37.67701268  1.47976427  .012142511  .261156175  2.46144116
     9.3    37.21414972  1.47883570  .013519543  .188821468  2.33983723
    10.2    37.21220743  1.47836592  .011656238  .189533108  2.33827523
    11.1    37.20982735  1.47839715  .011825326  .191019881  2.33578500
    12.1    37.20394340  1.47846979  .012242937  .200002735  2.32328453
    13.1    37.20392199  1.47853047  .012491521  .199993703  2.32356555
    14.1    37.20392157  1.47852346  .012463100  .200000416  2.32353000
    15.1    37.20392157  1.47852306  .012461475  .200000001  2.32352940

Run stopped after 15 major iterations.
Optimal solution found.


Nonlinear Regression Summary Statistics     Dependent Variable TOOTHDEF

  Source                 DF  Sum of Squares  Mean Square

  Regression              4      101.54608       25.38652
  Residual               59       37.20392         .63057
  Uncorrected Total      63      138.75000

  (Corrected Total)      62       91.60317

  R squared = 1 - Residual SS / Corrected SS =     .59386

                                           Asymptotic 95 %
                          Asymptotic     Confidence Interval
  Parameter   Estimate    Std. Error     Lower         Upper

  ED         1.478523059  7.91294E+13 -1.58338E+14  1.58338E+14
  GSD         .012461475  7.03428E+14 -1.40756E+15  1.40756E+15
  EMIN        .200000001   .125556256  -.051237488   .451237490
  EMAX       2.323529400   .192594506  1.938148684  2.708910116

  Asymptotic Correlation Matrix of the Parameter Estimates

                  ED       GSD      EMIN      EMAX

  ED          1.0000    1.0000     .0000     .0000
  GSD         1.0000    1.0000     .0000     .0000
  EMIN         .0000     .0000    1.0000     .0000
  EMAX         .0000     .0000     .0000    1.0000




Constrained Nonlinear Regression

Notes

 | -------------------------------------------- | ------------------------------------------------------ | 
 | Output Created                               | 22-APR-2002 18:03:45                                   | 
 | -------------------------------------------- | ------------------------------------------------------ | 
 | Comments                                     |                                                        | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 
 | Input       | Data                           | N:\YTO\TCDD\ABC kannat\SPSS\s242_abc_spss.sav          | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | Filter                         | WLC                                                    | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | Weight                         | <none>                                                 | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | Split File                     | <none>                                                 | 
 |             | ------------------------------ | ------------------------------------------------------ | 
 |             | N of Rows in Working Data File | 54                                                     | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 
 | Syntax                                       | MODEL PROGRAM ED=1 GSD=.5 EMIN=0 EMAX=3 .              | 
 |                                              | COMPUTE PRED_ =                                        | 
 |                                              | emin+(emax-emin)*(CDF.NORMAL(lg10(dose),ed,gsd)).      | 
 |                                              | CNLR toothdef                                          | 
 |                                              | /OUTFILE='C:\TEMP\spss158\SPSSFNLR.TMP'                | 
 |                                              | /PRED PRED_                                            | 
 |                                              | /BOUNDS ED <= 4; ED >= -2; GSD <= 50; GSD >= .01; EMIN | 
 |                                              | >= 0                                                   | 
 |                                              | /CRITERIA STEPLIMIT 2 ISTEP 1E+20 .                    | 
 |                                              |                                                        | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 
 | Resources   | Elapsed Time                   | 0:00:00.06                                             | 
 | ----------- | ------------------------------ | ------------------------------------------------------ | 


All the derivatives will be calculated numerically.




  Iteration Residual SS          ED         GSD        EMIN        EMAX

     0.3    31.52677442  1.00000000  .500000000  .000000000  3.00000000
     1.7    26.19381429  .946442255  .730244624  .550579902  2.94490523
     2.3    25.77987804  1.01880073  .744139368  .574005216  2.84761314
     3.3    24.90876215  .975768012  .555967150  .582118281  2.70798814
     4.2    24.55561980  .879083210  .535299912  .494986022  2.56522009
     5.1    24.11537699  .998746807  .409860209  .454290749  2.72353008
     6.1    24.05062195  .982757884  .487283086  .450225474  2.69999155
     7.1    24.03063943  .962505923  .456902219  .464382371  2.65123967
     8.1    24.02370648  .969520703  .440474141  .463834949  2.65977823
     9.1    24.02361942  .969663170  .443096935  .463305877  2.66103786
    10.1    24.02361814  .969466326  .442849238  .463352441  2.66059702
    11.1    24.02361812  .969494192  .442851166  .463354985  2.66063704

Run stopped after 11 major iterations.
Optimal solution found.


Nonlinear Regression Summary Statistics     Dependent Variable TOOTHDEF

  Source                 DF  Sum of Squares  Mean Square

  Regression              4      101.72638       25.43160
  Residual               50       24.02362         .48047
  Uncorrected Total      54      125.75000

  (Corrected Total)      53       62.37500

  R squared = 1 - Residual SS / Corrected SS =     .61485

                                           Asymptotic 95 %
                          Asymptotic     Confidence Interval
  Parameter   Estimate    Std. Error     Lower         Upper

  ED          .969494192   .163499982   .641094814  1.297893571
  GSD         .442851166   .214612064   .011790151   .873912182
  EMIN        .463354985   .132051691   .198121359   .728588612
  EMAX       2.660637039   .320442395  2.017009546  3.304264531

  Asymptotic Correlation Matrix of the Parameter Estimates

                  ED       GSD      EMIN      EMAX

  ED          1.0000     .2957     .2201     .6519
  GSD          .2957    1.0000    -.3231     .6035
  EMIN         .2201    -.3231    1.0000    -.1105
  EMAX         .6519     .6035    -.1105    1.0000

